Download mathematics project class: 10a

MATHEMATICS PROJECT
CLASS: 10A
TOPIC: ANGLES IN THE SAME SEGMENT OF A CIRCLE ARE EQUAL
OBJECTIVE: To verify that the angle in the same segment of a circle are equal using the method of cutting,
pasting and folding.
MATERIALS REQUIRED:
1.
2.
3.
4.
5.
6.
7.
8.
Geometry box
Practical workbook
Coloured chart papers – yellow, blue and red
Scissors
Scale
Sketch pen
Adhesives or glue sticks
Tracing papers – 2
PROCEDURE:
1. Draw a circle of 5 cm radius on a blue coloured chart paper. Use black sketch pen for drawing.
2. Cut out the circle.
3. Take a yellow chart paper. Cut it in the size of an A4 sheet and paste the circle on it.
4. Fold the circle in any way such that a chord is made. Draw the line segment AB.
5. Take two points P and Q on the circle in the same segment.
6. Form a crease joining AP. Draw AP.
7. Form a crease joining BP. Draw BP.
8. ∠𝐴𝑃𝐵 is formed in the major segment.
9. Form a crease joining AQ Draw AQ.
10. Form a crease joining BQ. Draw BQ.
11. ∠𝐴𝑄𝐵 is formed in the major segment.
12. Place tracing paper on the circle and draw a replica of the ∠𝐴𝑃𝐵 and ∠𝐴𝑄𝐵. Prepare two such replicas
of ∠𝐴𝑃𝐵 with green or red chart papers.
13. Place the cutout of ∠𝐴𝑃𝐵 on ∠𝐴𝑄𝐵. Stick the other replica along the edge BQ.
RESULT:
It is noted that ∠𝐴𝑃𝐵 = ∠𝐴𝑄𝐵 and these angles are in the same segment. ∠𝐴𝑃𝐵 is completely covered with
∠𝐴𝑄𝐵 and thus the theorem is verified.
LAST DATE OF SUBMISSION OF PROJECT: 28th November, 2014
TOPIC: (i) SUM OF EITHER PAIR OF OPPOSITE ANGLES OF A CYCLIC
QUADRILATERAL IS 180O (ii) IN A CYCLIC QUADRILATERAL THE EXTERIOR
ANGLE IS EQUAL TO THE INTERIOR OPPOSITE ANGLE
OBJECTIVE: To verify that the (i) sum of either pair of opposite angles of a cyclic quadrilateral is 180o (ii)
in a cyclic quadrilateral the exterior angle is equal to the interior opposite angle materials required
MATERIALS REQUIRED:
1.
2.
3.
4.
5.
6.
7.
8.
Geometry box
Practical workbook
Coloured chart papers – yellow, blue and pink
Scissors
Scale
Sketch pen
Adhesives or glue sticks
Tracing papers – 2
PROCEDURE:
1. Draw a circle of 5 cm radius on a blue coloured chart paper. Use black sketch pen for drawing.
2. Cut out the circle.
3. Take a yellow chart paper. Cut it in the size of an A4 sheet and paste the circle on it.
4. By paper folding get the chords AB, BC, CD and DA.
5. Draw the line segments AB, BC, CD and DA. Cyclic quadrilateral ABCD is obtained.
6. Make a replica of cyclic quadrilateral ABCD using a tracing paper. Now draw the quadrilateral on the
pink chart paper with the help of tracing paper and cut it out.
7. Now cut the quadrilateral in 4 parts such that each part contain one angle like ∠𝐴, ∠𝐵, ∠𝐶, ∠𝐷.
8. Place ∠𝐴 and ∠𝐶 adjacent to each other.
9. Produce AB to form a ray AE. Exterior ∠𝐶𝐵𝐸 is formed.
10. Place the replica of D on ∠𝐶𝐵𝐸.
RESULT:
It is noted that when ∠𝐴 and ∠𝐶 are placed adjacent to each other they form a linear pair: ∠𝐴 + ∠𝐶 = 180o.
Also, ∠𝐷 completely covers ∠𝐶𝐵𝐸. This shows that the exterior angle of a cyclic quadrilateral ABCD is equal
to the opposite interior angle.
LAST DATE OF SUBMISSION OF PROJECT: 28th November, 2014